There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

DNA sequencing with chain terminating inhibitors

The vast majority of coding variants are rare, and assessment of the contribution of rare variants to complex traits is hampered by low statistical power and limited functional data. Improved methods for predicting the pathogenicity of rare coding variants are needed to facilitate the discovery of disease variants from exome sequencing studies. We developed REVEL (rare exome variant ensemble learner), an ensemble method for predicting the pathogenicity of missense variants on the basis of individual tools: MutPred, FATHMM, VEST, PolyPhen, SIFT, PROVEAN, MutationAssessor, MutationTaster, LRT, GERP, SiPhy, phyloP, and phastCons. REVEL was trained with recently discovered pathogenic and rare neutral missense variants, excluding those previously used to train its constituent tools. When applied to two independent test sets, REVEL had the best overall performance (p −12 ) as compared to any individual tool and seven ensemble methods: MetaSVM, MetaLR, KGGSeq, Condel, CADD, DANN, and Eigen. Importantly, REVEL also had the best performance for distinguishing pathogenic from rare neutral variants with allele frequencies

REVEL: An Ensemble Method for Predicting the Pathogenicity of Rare Missense Variants

Standards and Guidelines for the Interpretation and Reporting of Sequence Variants in Cancer: A Joint Consensus Recommendation of the Association for Molecular Pathology, American Society of Clinical Oncology, and College of American Pathologists

The subtree max gap problem with application to parallel string covering

Faster index for property matching

Novel high throughput sequencing technology methods have redefined the way genome sequencing is performed. They are able to produce tens of millions of short sequences (reads) in a single experiment and with a much lower cost than previous sequencing methods. Due to this massive amount of data generated by the above systems, efficient algorithms for mapping short sequences to a reference genome are in great demand. In this paper, we present a practical algorithm for addressing the problem of efficiently mapping uniquely occuring short reads to a reference genome. This requires the classification of these short reads into unique and duplicate matches. In particular, we define and solve the Massive Exact Unique Pattern Matching problem in genomes.

Mapping uniquely occurring short sequences derived from high throughput technologies to a reference genome

Approximate string matching is the problem of finding all factors of a text \(t\) of length \(n\) that are at a distance at most \(k\) from a pattern \(x\) of length \(m\). Approximate circular string matching is the problem of finding all factors of \(t\) that are at a distance at most \(k\) from \(x\) or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time \(\mathcal {O}(n(k + \log m) /m)\). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using \(x\) and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach.

Costas S. Iliopoulos

Papers

The subtree max gap problem with application to parallel string covering

Faster index for property matching

Mapping uniquely occurring short sequences derived from high throughput technologies to a reference genome

Average-Case Optimal Approximate Circular String Matching

Finite automata based algorithms on subsequences and supersequences of degenerate strings